Cambridge International AS Level

Mathematics 9709

Pure mathematics, probability & statistics and mechanics, with flexible combinations of AS and A Level papers.

Exam year

Syllabus version: 2026–2027 syllabusChecked against the Cambridge syllabusExam year 2027 is covered by the 2026–2027 syllabus.

Subject review complete (19 Oct 2026). All 22 AS Level Mathematics questions were re-solved and checked against the syllabus and Cambridge mark-scheme conventions, and their auto-marking was tested with correct and incorrect answers.

Weighting by paper. Some papers are alternatives (for example Core or Extended, or practical or alternative to practical), so the figures add up to more than 100%.

Paper 1 Pure Mathematics 160%
Paper 2 Pure Mathematics 240%
Paper 4 Mechanics40%
Paper 5 Probability & Statistics 140%

Original questions22

Topics covered4/4

Papers4

Mock papers4

What is assessed

4 components. Question formats: structured.

Paper 1 Pure Mathematics 1AS

1 h 50 min75 marks60% of AS

10 to 12 structured questions on the Pure Mathematics 1 content; compulsory for both AS Level and A Level and the foundation for every other paper.

What the paper looks like

About 10–12 compulsory questions, 75 marks in 1 h 50 min. Early questions are short (3–5 marks); later ones are multi-part (8–11 marks) blending topics, e.g. functions with transformations or calculus with coordinate geometry. Command words: find, show that, solve, sketch, determine. Exact answers often requested; otherwise 3 s.f. or 1 d.p. for degrees. Calculator allowed but full working required.

StructuredList of formulae and statistical tables (MF19) provided

Checked against the Cambridge syllabus

Paper 2 Pure Mathematics 2AS option

1 h 15 min50 marks40% of AS

6 to 8 structured questions on the Pure Mathematics 2 content; offered only as part of AS Level.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min. Typical parts are 2–5 marks: modulus equations, factor theorem with unknown coefficients, logarithmic linearisation from a given line, R-form trigonometry, calculus of exponentials/trig, trapezium rule and iteration. Frequent “show that” parts give an answer to carry forward.

StructuredList of formulae and statistical tables (MF19) provided

Checked against the Cambridge syllabus

Paper 4 MechanicsAS option

1 h 15 min50 marks40% of AS

6 to 8 structured questions on the Mechanics content; may be taken as part of AS Level or A Level.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min, mostly numerical with g = 10. Questions use diagrams of particles on planes, strings over pulleys or vehicles with power; parts of 2–6 marks ask to find forces, accelerations, speeds or distances. Answers to 3 s.f. (angles 1 d.p.); a clear force diagram is expected.

StructuredList of formulae and statistical tables (MF19) provided; take g = 10 m s⁻²

Checked against the Cambridge syllabus

Paper 5 Probability & Statistics 1AS option

1 h 15 min50 marks40% of AS

6 to 8 structured questions on the Probability & Statistics 1 content; compulsory for A Level and an AS option.

What the paper looks like

6–8 compulsory questions, 50 marks in 1 h 15 min. Data questions with stem-and-leaf, box plots, histograms or summary totals; counting problems with cases; tree-diagram conditional probability; binomial and geometric models; normal distribution with unknown parameters and normal approximation. Parts are usually 1–5 marks; exact fractions are acceptable.

StructuredList of formulae and statistical tables (MF19) provided

Checked against the Cambridge syllabus

Assessment overview

From the 2026–2027 syllabus. Checked against the Cambridge syllabus

AS Level (Route 1a): Pure 1 + Probability & Statistics 1

Paper 1Paper 5

All AS components taken in the same series.

AS Level (Route 1b): Pure 1 + Mechanics

Paper 1Paper 4

All AS components taken in the same series.

AS Level (Route 1c): Pure 1 + Pure 2

Paper 1Paper 2

This AS option cannot count towards A Level.

Assessment objective	AS Level weighting
AO1 Knowledge and understanding	55%
AO2 Application and communication	45%

Changes in this syllabus version

No significant changes affecting teaching compared with the 2023–2025 syllabus; content, papers, timings and weightings are unchanged.
Version 2 (Nov 2024): headers on the assessment overview page updated.
Version 3 (Feb 2025): typographical errors in the subject content corrected.
Version 4 (Dec 2025): a weblink updated; specimen materials were not changed.

Command words used in Mathematics papers (11)

Calculate: Work out a result from the facts, figures or information given.
Describe: State the main points or give the key characteristics and features.
Determine: Establish a result with certainty, usually with supporting working.
Evaluate: Judge or calculate the value, amount, quality or importance of something.
Explain: Give reasons or purposes, making relationships clear, with supporting evidence.
Identify: Name, select or recognise.
Justify: Support a case or claim with evidence or argument.
Show (that): Give a structured chain of working that leads to a given result.
Sketch: Draw a simple freehand diagram showing key features, with care over proportion.
State: Express clearly and briefly, usually without working.
Verify: Confirm that a given statement or result is true.

Examiner guidance from recent reports (14)

Pure Mathematics 1. Calculator-only answers to quadratic or trigonometric equations lose method marks: write the factorisation, the completed square or the formula with values substituted, then the roots.

Pure Mathematics 1. In trigonometric equations, check the required interval and units before writing the final list; missing a second-quadrant solution or answering in degrees when radians were requested is a common way to drop the final accuracy mark.

Pure Mathematics 1. When a composite function is involved, state which function is applied first and check the range of the inner function lies in the domain of the outer one; for an inverse, restate it in terms of x and give its domain.

Pure Mathematics 1. For areas and volumes, sketch the region and find intersection points first; for a volume between two curves use π∫(y₁² − y₂²) dx, not π∫(y₁ − y₂)² dx.

Pure Mathematics 2. With R sin(θ + α) questions, give R exactly (e.g. √13) and α to at least 2 d.p. in working; rounding α early pushes the final angles outside the accepted range.

Pure Mathematics 2. For iterations, show each iterate to at least one more decimal place than required and continue until two successive values agree to the stated accuracy, or show a sign-change check.

Pure Mathematics 3. In implicit differentiation, products such as xy or x² ln y need the product rule; forgetting the dy/dx factor on terms in y is the most common lost mark.

Pure Mathematics 3. Complex numbers and vectors are often left blank late in the paper — practise them so they are reliable marks. Keep arguments in radians and in the range −π < θ ≤ π unless told otherwise.

Pure Mathematics 3. In binomial expansions with rational n, factor out the constant first, e.g. (2 + x)⁻¹ = ½(1 + x/2)⁻¹, and use brackets around terms like (−x/2)² to avoid sign errors.

Mechanics. Draw and label a force diagram before resolving; most errors come from a missing weight component or friction acting the wrong way. Take g = 10 and work to 4 s.f. before giving 3 s.f. answers.

Mechanics. If velocity or acceleration depends on time, use calculus — constant-acceleration formulae are not valid. For total distance, split the integral wherever the velocity changes sign.

Probability & Statistics 1. In counting problems, set out the separate cases in a list or table and add them; communication of which scenario each term represents earns method credit even if a slip occurs.

Probability & Statistics 1. In normal questions, show the standardisation with the values substituted and a sketch; when finding μ or σ, use z-values to 4 d.p. from the critical values table rather than rounded ones.

Probability & Statistics 2. Hypothesis-test conclusions must be in context and non-assertive, e.g. “there is evidence at the 5% level that the mean has decreased”, and must compare like with like (probability vs significance level, or statistic vs critical value).

Topic map

Practice types

Free sample questions

FAQs

Are these official 9709 past-paper questions?

No. They are original questions written to match the Mathematics syllabus topics. Official past papers are available to schools through Cambridge.

Why choose an exam year?

Cambridge updates syllabuses periodically. Your exam year selects the matching configuration so topics and components follow the right version.

How do AS and A Level differ here?

Both pathways share code 9709. AS pages include AS topics and components only; A Level pages add the A Level content and papers.

Is a calculator allowed?

In this configuration a scientific calculator is permitted for the listed papers. Check your syllabus for the exact rule.